Strain pseudospins with power-law interactions: Glassy textures of a cooled coupled-map lattice

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 14, 2008, Pages

  Shenoy, S R ^a,b   Lookman, T ^c,d  

^a UNIVERSITY OF HYDERABAD   (India)

^b ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

^d UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54449088346     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.144103     Document Type: Article

References (72)

1. K. Binder and W. Kob, Glassy Materials and Disordered Solids (World Scientific, Singapore, 2005)
2. Z. Nishiyama, Martensitic Transformations (Academic, New York, 1978).
3. W. Kauzmann, Chem. Rev. (Washington, D.C.) CHREAY 0009-2665 10.1021/cr60135a002 43, 219 (1948).
4. F. H. Stillinger and T. A. Weber, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.25.978 25, 978 (1982)
5. S. Sastry, P. G. Debenedetti, and F. H. Stillinger, Nature (London) NATUAS 0028-0836 10.1038/31146 393, 554 (1998).
6. C. Donati, J. F. Douglas, W. Kob, S. J. Plimpton, P. H. Poole, and S. C. Glotzer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2338 80, 2338 (1998).
7. C. Dasgupta, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/20/2/007 20, 131 (1992)
8. C. Dasgupta, Pramana PRAMCI 0304-4289 10.1007/BF02704576 64, 679 (2005).
9. G. R. Barsch, B. Horovitz, and J. A. Krumhansl, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.1251 59, 1251 (1987)
10. B. Horovitz, G. R. Barsch, and J. A. Krumhansl, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.43.1021 43, 1021 (1991).
11. M. Baus and R. Lovett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.1781 65, 1781 (1990)
12. M. Baus and R. Lovett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.44. 1211 44, 1211 (1991).
13. S. Kartha, T. Castán, J. A. Krumhansl, and J. P. Sethna, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.3630 67, 3630 (1991)
14. S. Kartha, J. A. Krumhansl, J. P. Sethna, and L. K. Wickham, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.803 52, 803 (1995).
15. S. R. Shenoy, T. Lookman, A. Saxena, and A. R. Bishop, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.R12537 60, R12537 (1999)
16. K. O. Rasmussen, T. Lookman, A. Saxena, A. R. Bishop, R. C. Albers, and S. R. Shenoy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.055704 87, 055704 (2001)
17. T. Lookman, S. R. Shenoy, K. O. Rasmussen, A. Saxena, and A. R. Bishop, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.024114 67, 024114 (2003)
18. D. M. Hatch, T. Lookman, A. Saxena, and S. R. Shenoy, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.104105 68, 104105 (2003).
19. S. R. Shenoy, T. Lookman, and A. Saxena, in Magnetism and Structure in Functional Materials, Springer Series in Materials Science, edited by, A. Planes,,, L. Manosa,, and, A. Saxena, (Springer, New York, 2005).
20. Y. Wang, X. Ren, and K. Otsuka, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.225703 97, 225703 (2006).
21. H. Shintani and H. Tanaka, Nat. Phys. ZZZZZZ 1745-2473 2, 200 (2006)
22. P. Harrowell, Nat. Phys. ZZZZZZ 1745-2473 2, 157 (2006).
23. S. Prosandeev and L. Bellaiche, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.094102 75, 094102 (2007).
24. J. D. Shore, M. Holzer, and J. P. Sethna, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.11376 46, 11376 (1992).
25. A. Cavagna, I. Giardina, and T. S. Grigera, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00247-9 61, 74 (2003)
26. P. Dimopoulos, D. Espriu, E. Jane', and A. Prats, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.056112 66, 056112 (2002).
27. P. Bak, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.46.791 46, 791 (1981).
28. J. Bechhoefer, H. Löwen, and L. S. Tuckerman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.1266 67, 1266 (1991).
29. J. Schmalian and P. G. Wolynes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.836 85, 836 (2000).
30. Dynamics and Thermodynamics of Systems with Long-Range Interactions, Lecture Notes in Physics Vol. 602, edited by, T. Dauxois,,, S. Ruffo,,, E. Arimondo,, and, M. Wilkens, (Springer, New York, 2002)
31. A. Rapisarda and A. Pluchino, Europhys. News 36, 202 (2005). 0531-7479
32. E. Bayong, H. T. Diep, and V. Dotsenko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.14 83, 14 (1999).
33. F. Ritort, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.1190 75, 1190 (1995)
34. M. L. Mansfield, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.016101 66, 016101 (2002).
35. J. P. Garrahan and D. Chandler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.035704 89, 035704 (2002)
36. M. Sellitto, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/14/7/305 14, 1455 (2002).
37. D. Elderfield and D. Sherrington, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/16/32/006 16, L1169 (1983)
38. A. Erzan and E. Lage, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/16/ 17/002 16, L555 (1983).
39. M. Tarzia and M. A. Moore, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.031502 75, 031502 (2007).
40. T. Lookman, S. R. Shenoy, and A. Saxena, Bull. Am. Phys. Soc. BAPSA6 0003-0503 49 (1), 1315 (2004).
41. M. Blume, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.141.517 141, 517 (1966)
42. H. W. Capel, Physica (Amsterdam) PHYSAG 0031-8914 10.1016/0031-8914(66) 90027-9 32, 966 (1966)
43. M. Blume, V. J. Emery, and R. B. Griffiths, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.4.1071 4, 1071 (1971).
44. J. Crutchfield and K. Kaneko, in Directions in Chaos, edited by, Hao Bai-Lin, (World Scientific, Singapore, 1987), Vol. 2
45. K. Kaneko, Physica D PDNPDT 0167-2789 10.1016/0167-2789(90)90119-A 41, 137 (1990).
46. C. S. Burns, R. A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms (Prentice-Hall, Englewood Cliffs, NJ, 1998)
47. C. Chandre, S. Wiggins, and T. Uzer, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(03)00117-9 181, 171 (2003).
48. We note that (a) the strains Eμν = eμν + gμν that enter the free energy actually depend on, eμν, the symmetric part of the distortion tensor plus a "geometric nonlinearity" part, gμν, quadratic in the symmetrized distortion and in local rotations. We work in the limit that the geometric nonlinearity is negligible, so the linearized strain is the symmetrized distortion. We can thus loosely refer to a "strain representation," although strictly speaking, it is a "distortion representation." The compatibility constraint actually applies to the distortion tensor (Ref.). (b) The definitions in Eqs. 2.1 2.4 of e3 =2 Exy and O3 = Kx Ky have factors of 2 and 1/2 compared to earlier work (Refs.). The compatibility condition has the product O3 e3 and so is unchanged.
49. S. R. Shenoy, T. Lookman, and A. Saxena (unpublished).
50. E. Vives, J. Goicoechea, J. Ortin, and A. Planes, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.R5 52, R5 (1995)
51. P. A. Lindgard and O. G. Mouritsen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.57.2458 57, 2458 (1986).
52. N. Shankaraiah, K. P. N. Murthy, S. R. Shenoy, and T. Lookman (unpublished).
53. Variational distributions diagonal in coordinate space (Ref.) are clearly inappropriate in our spatially nonlocal PLA model. A purely uniform mean field would yield a slightly different self-consistency equation.
54. S. C. Manrubia and A. S. Mikhailov, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2000-00309-6 50, 580 (2000)
55. S. C. Manrubia and A. S. Mikhailov, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2001-00262-4 53, 451 (2001)
56. M. G. Cosenza and A. Parravano, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.036224 64, 036224 (2001).
57. S. Sinha, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.016209 66, 016209 (2002).
58. S. N. Behera and A. Khare, Pramana PRAMCI 0304-4289 10.1007/BF02847222 15, 245 (1980)
59. F. Falk, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01308772 51, 177 (1983)
60. U. Roy, R. Atre, C. Sudheesh, C. N. Kumar, and P. K. Panigrahi, arXiv:0708.3646 (unpublished).
61. S. R. Shenoy and G. S. Agarwal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.29.1315 29, 1315 (1984)
62. K. P. N. Murthy and S. R. Shenoy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.36.5087 36, 5087 (1987).
63. E. Vives, J. Ortín, L. Mañosa, I. Ràfols, R. Pérez-Magrané, and A. Planes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.1694 72, 1694 (1994).
64. V. Hardy, A. Maignan, S. Hébert, C. Yaicle, C. Martin, M. Hervieu, M. R. Lees, G. Rowlands, D. Mc K. Paul, and B. Raveau, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.220402 68, 220402 (2003)
65. W. Wu, C. Israel, N. Hur, S. Park, S.-W. Cheong, and A. de Lozanne, Nature Mater. NMAACR 1476-1122 10.1038/nmat1743 5, 881 (2006)
66. P. Chaddah, K. Kumar, and A. Banerjee, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.100402 77, 100402 (R) (2008).
67. T. Balcerzak and J. W. Tucker, J. Magn. Magn. Mater. JMMMDC 0304-8853 10.1016/j.jmmm.2003.11.377 278, 87 (2004).
68. A. Torcini and S. Lepri, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.R3805 55, R3805 (1997).
69. S. Alexander, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(97)00069-0 296, 65 (1998).
70. H. Tanaka, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.479596 111, 3163 (1999).
71. P. W. Anderson, B. Halperin, and C. M. Varma, Philos. Mag. PHMAA4 0031-8086 10.1080/14786437208229210 25, 1 (1972)
72. W. A. Phillips, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/BF00660072 7, 351 (1972).